1. Field of the Invention
The present invention relates to communication systems. More specifically, the present invention relates to modulation schemes utilized in mobile communications systems.
While the present invention is described herein with reference to a particular embodiment for an illustrative application, it is understood that the invention is not limited thereto. Those of ordinary skill in the art having access to the teachings provided herein will recognize additional modifications, applications and embodiments within the scope thereof.
2. Description of the Invention
Mobile communications systems are typified by the movement of a receiver relative to a transmitter or visa versa. The communications link between transmitters and receivers in mobile communications systems is characterized as a fading channel. Mobile satellite communications systems, having a transmitter on a spacecraft and a receiver on a ground based vehicle, cellular telephone systems and terrestrial microwave systems are examples of fading communications systems. A fading channel is a channel which is severely degraded. The degradation is due to numerous effects including multipath fading, severe attenuation due to the receipt via multiple paths of reflections of the transmitted signal off objects and structures in the atmosphere and on the surface. Other effects contributing to the impairment of the faded channel include doppler shift due to the movement of the receiver relative to the transmitter and additive noise.
A need has been recognized for a joint modulation coding scheme which would allow for the effective transmission of data over the faded channel at a desired bit/error rate within a reasonable signal-to-noise ratio. Ideally, the scheme would also provide simultaneously bandwidth efficiency and power efficiency.
As discussed by G. Ungerboeck, in "Channel Coding with Multilevel/Phase Signals", IEEE Transactions on Information Theory, Vol. IT-28, No. 1, January 1982, pp. 55-67, conventional trellis codes have heretofore provided an adequate modulation scheme for Gaussian channels, those characterized by noise only without multipath fading and doppler shift. Conventional trellis coded modulation (TCM) refers to the technique wherein a rate n/(n+1) trellis code is combined (through a suitable mapping function) with an M=2.sup.n+1 point signal constellation to produce a coded modulation which has no bandwidth expansion relative to an uncoded 2.sup.n point modulation of the same type yet gives significant performance improvement.
Conventional systems have traditionally employed symmetric signal constellations, i.e., those with uniformly spaced signal points. Although symmetric signal constellations are optimum for uncoded systems, the same is not necessarily true for TCM systems. In fact, it has been shown that by designing the signal constellations to be asymmetric, one can, in many instances, obtain a performance gain over the traditional symmetric TCM design. See: (1) "Asymmetric MPSK for Trellis Codes", by D. Divsalar and J. H. Yuen, in GLOBECOM '84 Proceedings, Atlanta, Ga., Nov. 26-29, 1984, pp. 20.6.1-20.6.8; (2) "Combined Trellis Coding with Asymmetric MPSK Modulation", by M. K. Simon and D. Divsalar, in JPL Publication 85-24, Pasadena, Calif., May 1, 1985; and "Trellis Coding with Asymmetric Modulations", by D. Divsalar, M. K. Simon, and J. H. Yuen, published in February 1987 in the IEEE Transactions on Communications.
Performance gain, both in measure and in degree, is, in general, a function of many factors: signal-to-noise ratio (SNR), complexity of the trellis encoder (number of trellis code states), and the number of modulation levels (M). For TCM systems, an asymptotic measure of performance gain is the comparison of the minimum free Euclidean distance d.sub.free of the trellis code relative to the minimum distance d.sub.min of the uncoded modulation. The term "asymptotic performance gain" refers to the performance gain in the vicinity of the value of energy-to-noise ratio E.sub.b /N.sub.o at which the probability of error P.sub.b becomes very small, i.e., less than 10.sup.-8. This performance measure is an indication of the maximum reduction in required bit energy-to-noise spectral density ratio E.sub.b /N.sub.o with respect to an uncoded system that can be achieved for arbitrarily small system bit error rates. At practical bit error rates, i.e., 10.sup.-3 to 10.sup.-5 this measure can often be misleading since the "real" gain in E.sub.b /N.sub.o reduction due to coding and asymmetry, could be significantly less. More important, however, is the fact that in certain cases of asymmetry, the asymptotic improvement, as measured by d.sub.free, can only be achieved in the limit as points in the signal constellation merge together, i.e., the trellis code becomes catastrophic. Thus, at some point, conventional trellis coded modulation schemes may not be improved further without the code becoming catastrophic, at which point it would be unable to accurately modulate and demodulate input data.
In the past, trellis codes have been designed for the additive white gaussian noise (AWGN) channel. These codes have been used for systems operating over fading channels although they may not be optimum on these channels. More importantly, it can be shown that most high throughput optimum trellis codes that have been used thus far for the AWGN channel, in particular, those with parallel paths, will either provide no performance gain or provide worse performance gain with respect to an uncoded system.
There is therefore a need in the art for a modulation scheme which would provide performance gains over that obtainable via conventional trellis coded modulation schemes. There is a concomitant need for a criteria by which the performance of the improved scheme may be evaluated and a design procedure, in accordance with the criteria, by which modulation codes and suitable transmitter structures may be generated to satisfy such performance criteria.